Distributed learning of composite machine learning models

ABSTRACT

Computer-implemented techniques for learning composite machine learned models are disclosed. Benefits to implementors of the disclosed techniques include allowing non-machine learning experts to use the techniques for learning a composite machine learned model based on a learning dataset, reducing or eliminating the explorative trial and error process of manually tuning architectural parameters and hyperparameters, and reducing the computing resource requirements and model learning time for learning composite machine learned models. The techniques improve the operation of distributed learning computing systems by reducing or eliminating straggler effects and by reducing or minimizing synchronization latency when executing a composite model search algorithm for learning a composite machine learned model.

TECHNICAL FIELD

The present disclosure relates to machine learning. More particularly,the present disclosure relates to computer-implemented techniques fordistributed learning of composite machine learning models.

BACKGROUND

In recent years, machine learning techniques have achieved remarkablyimproved performance in several areas. With such improvements, machinelearning techniques are now being used to provide business andenterprise solutions. For example, within an online professionalnetwork, machine learning techniques may be used to recommend jobs auser might be interested in, to suggest other professionals in thenetwork to connect with, for natural language processing tasks, or forother tasks. Given the early successes applying machine learningtechniques in the business and enterprise domains, their use in thosedomains can only be expected to increase in the future.

Unfortunately, applying machine learning techniques can be humanintensive, requiring great technical expertise. Not all businesses andorganizations have the resources to hire experienced and qualifiedmachine learning engineers. Even if experts are available, theperformance of a machine learning technique at a given task can be quitesensitive to the tuning of many architectural parameters andhyperparameters. Exploration of different machine learning techniquescan require significant computing resources. This requirement is asignificant challenge today in the era of “big data” with gigabyte,terabyte and even petabyte-scale learning datasets.

Disclosed embodiments address these and other issues.

The approaches described in this section are approaches that could bepursued, but not necessarily approaches that have been previouslyconceived or pursued. Therefore, unless otherwise indicated, it shouldnot be assumed that any of the approaches described in this sectionqualify as prior art, or are well-understood, routine, or conventional,merely by virtue of their inclusion in this section.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 shows a composite machine learning model, according to somedisclosed embodiments.

FIG. 2 illustrates a model of an artificial neuron, according to somedisclosed embodiments.

FIG. 3 depicts a multi-layer feedforward artificial neural network,according to some disclosed embodiments.

FIG. 4 illustrates a distributed learning computing system, according tosome disclosed embodiments.

FIG. 5 is a flowchart of a process performed by a worker in adistributed learning computing system, according to some disclosedembodiments.

FIG. 6 is a flowchart of a process performed by a parameter sever in adistributed learning computing system, according to some disclosedembodiments.

FIG. 7 illustrates a high-level architecture of a distributed learningcomputing system, according to some disclosed embodiments.

FIG. 8 is a flowchart of an algorithm for learning a composite machinelearning model, according to some disclosed embodiments.

FIG. 9A shows an example composite neural network and an examplesub-neural network candidate pool after an iteration of a compositeneural network search algorithm, according to some disclosedembodiments.

FIG. 9B shows an example composite neural network where all of thesub-neural networks in an example candidate pool are learned separatelyat an iteration of a composite neural network search algorithm,according to some disclosed embodiments.

FIG. 9C shows an example composite neural network and an examplecandidate pool at an iteration of a composite neural network searchalgorithm, according to some disclosed embodiments.

FIG. 9D illustrates how new sub-neural networks are selected andgenerated in a next candidate pool from one iteration of a compositeneural network search algorithm to the next iteration of the algorithm,according to some disclosed embodiments.

FIG. 10A depicts an ideal execution of a composite model searchalgorithm on a group of worker computing nodes in a distributed learningsystem, according to some disclosed embodiments.

FIG. 10B depicts a practical execution of a composite model searchalgorithm on a group of worker computing nodes in a distributed learningsystem, according to some disclosed embodiments.

FIG. 11A depicts an execution of a composite model search algorithm on agroup of worker computing nodes in a distributed learning systemaccording to a conventional distributed learning strategy, according tosome disclosed embodiments.

FIG. 11B depicts an execution of a composite model search algorithm on agroup of worker computing nodes in a distributed learning systemaccording to a network-level asynchronous distributed learning strategy,according to some disclosed embodiments.

FIG. 12 depicts a straggler effect that can occur when executing acomposite model search algorithm on a group of worker computing nodes ina distributed learning system according to a network-level asynchronousdistributed learning strategy, according to some disclosed embodiments.

FIG. 13A depicts sub-model learning early start when executing aniteration of a composite model search algorithm on a group of workercomputing nodes in a distributed learning system according to anetwork-level asynchronous distributed learning strategy, according tosome disclosed embodiments.

FIG. 13B depicts sub-model learning early start when executing aniteration of a composite model search algorithm on a group of workercomputing nodes in a distributed learning system according to anetwork-level asynchronous distributed learning strategy, according tosome disclosed embodiments.

FIG. 14 illustrates network communications between a task scheduler of aworker group in a distributed learning system and a worker in the workergroup implementing the network-level asynchronous distributed learningstrategy, according to some embodiments.

FIG. 15 is a block diagram that illustrates a computing device upon usedin some disclosed embodiments.

DETAILED DESCRIPTION

In the following description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of embodiments of the present invention. It will beapparent, however, that embodiments of the present invention may bepracticed without these specific details. In other instances, somestructures and devices are shown in block diagram form in order to avoidunnecessarily obscuring embodiments of the present invention.

General Overview

Computer-implemented techniques for learning composite machine learnedmodels are disclosed. Benefits to implementors of the disclosedtechniques include allowing non-machine learning experts to use thetechniques for learning a composite machine learned model based on alearning dataset, reducing or eliminating the explorative trial anderror process of manually tuning architectural parameters andhyperparameters, and reducing the computing resource requirements andmodel learning time for learning composite machine learned models. Thetechniques improve the operation of distributed learning computingsystems by reducing or eliminating straggler effects and by reducing orminimizing synchronization latency when executing a composite modelsearch algorithm for learning a composite machine learned model.

Composite Machine Learned Models

The disclosed techniques may be used to learn a composite machinelearned model as a composite of sub-machine learned models with theability to scale to learning datasets containing potentially thousandsto billions of learning examples. Before discussing the techniques ingreater detail, some terminology will be discussed. The followingdefinitions are offered for purposes of illustration, not limitation, inorder to assist with understanding the discussion that follows.

As used herein, the term “learning dataset” may encompass a set offeature vectors where each feature vector may encompass a description ofan object by using a set of features. The number of features of alearning dataset is sometimes referred to as the dimension ordimensionality of the learning dataset. A feature vector is sometimesreferred to as an “example,” in the context of learning a model, and a“sample,” in the context of generating an inference or prediction usinga learned model.

As used herein, the term “machine learned model,” or just “model,” mayencompass an inference or predictive model constructed or discoveredfrom a learning dataset by a machine learning algorithm, such as, forexample, a regression algorithm (e.g., linear regression, logisticregression, etc.), an artificial neural network algorithm (e.g.,perceptron, multilayer perceptron, back-propagation, stochastic gradientdescent, etc.), or a deep learning algorithm (e.g., a convolutionalneural network).

The process of generating a machine learned model from a learningdataset is sometimes referred to as “learning.” Learning a machinelearned model can occur in different learning settings, including in asupervised learning setting, an unsupervised learning setting, or in asemi-supervised setting. In supervised learning, a goal may be to inferthe value of a target feature on unseen samples where a machine learnedmodel is learned using labeled examples. In contrast, unsupervisedlearning may not rely on labeled examples when learning a machinelearned model. Instead, a goal of unsupervised learning may be todiscover some inherent distributional information in the learningdataset such as, for example, the cluster structure of a set of datapoints. With semi-supervised learning, there is a mixture of labeled andunlabeled examples in the learning dataset.

As used herein, the term “composite machine learned model, or just“composite model,” may encompass a machine learned model that isconstructed from a combination of a set of sub-machine learned models(“sub-models”). FIG. 1 shows a possible composite model architecture,according to some disclosed embodiments. The composite model contains anumber of sub-models (e.g., Base Learner-1, Base Learner-2, . . . , BaseLearner-N) which are sometimes called “base” learners. A base learnermay be generated from a learning dataset according to a base machinelearning algorithm which can be, for example, a regression algorithm(e.g., linear regression, logistic regression, etc.), an artificialneural network algorithm (e.g., perceptron, multilayer perceptron,back-propagation, stochastic gradient descent, etc.), or a deep learningalgorithm (e.g., a convolutional neural network). Different baselearners may be generated according to different base machine learningalgorithms.

As used herein, the term “artificial neural network,” or just “neuralnetwork,” may encompass computerized simulations of biological neuralnetworks. The function of a neural network may be determined by themodel of an artificial neuron, the structure of the neural network, andthe machine learning algorithm. An artificial neuron in a neural networkis sometimes called a “unit.” A unit may be the basic computationcomponent in neural networks. A unit may be based on, for example, theMcCulloch-Pitts (M-P) model.

According to the M-P model, as depicted in FIG. 2, input signals (e.g.,X₁, X₂, and X₃) may be multiplied with corresponding connection weights(e.g., W₁, W₂, and W₃), and then signals may be aggregated and comparedwith a threshold or bias of the unit. If the aggregated signal is largerthan the bias, then the unit may be activated and generate an outputsignal according to an activation function (e.g., J(ΣX_(i)W_(i)−Θ)). Theunit maybe linked by weighted connections to form a network of units.Many different types of neural networks exist including multi-layerfeedforward neural networks.

A possible multi-layer feedforward neural network is shown in FIG. 3. Inthe neural network of FIG. 3, units are connected layer-by-layer, andthere may not be either intra-layer connections or cross-layerconnections. The neural network may include an input layer which mayreceive input feature vectors, where each unit of the input layer maycorrespond to one element of a feature vector. The activation functionfor an input unit may be the identity function f(x)=x. However, otheractivation functions for an input layer unit are possible. The outputlayer may output labels, where each unit in the output layer maycorrespond to a possible label, or an element of a label vector. Thelayers between the input layer and the output layer are sometimesreferred to as hidden layers. The neural network may have more than onehidden layer and such a neural network is sometimes referred to as adeep neural network. The units of the hidden and output layers may befunctional units that use a sigmoid function as the activation function.Other activation functions for a hidden layer or an output layer unitare possible.

A goal of learning a neural network may be to determine the values ofthe connection weights and the biases of the units. Once these valuesare determined, the function computed by the neural network may bedecided. The neural network may use differentiable activation functions,and the entire neural network may be optimized using a gradient descentmethod such as, for example, back-propagation. With back-propagation,the inputs may be feed-forwarded from the input layer via the hiddenlayer(s) to the output layer, at which the error is calculated bycomparing the network output with a ground-truth. Then, the error may beback propagated to the hidden layer(s) and the input layer, during whichthe connection weights and biases are adjusted to reduce the error. Theprocess may be accomplished by tuning towards the direction with thegradient. The process may be repeated for many rounds, until thetraining error is minimized of the training process is terminated toavoid overfitting.

While in some disclosed embodiments the techniques for learningcomposite machine learning models are applied in the supervised learningcontext to learn a composite deep artificial neural network composed ofmultiple sub-neural networks, the techniques are not so limited and maybe applied in an unsupervised learning context, a supervised learningcontext, or a semi-supervised learning context with other types ofmachine learning models including a combination of different machinelearning models. For example, the sub-models can be as simple as anif-statement, or as complex as convolutional or recurrent artificialneural networks.

Functional Overview

With the disclosed techniques, learning composite models from largelearning datasets is more automated, more efficient (with lesstrial-and-error performed by humans), and requires less expertise inarchitectural parameter and hyperparameter tuning required, compared tomore manual approaches. The disclosed techniques encompass compositemodel architecture search and hyperparameter tuning with reduced expertintervention in a distributed learning computing system.

An example distributed learning computing system is described in greaterdetail elsewhere in this disclosure. Briefly, however, the distributedlearning computing system may encompass one or more groups of “workers.”Each worker may execute on a computing device and the workers in a groupmay execute on a cluster of one or more computing devices. The one ormore computing devices may encompass one or more hardware processingunits. A hardware processing unit can be a central processing unit(CPU), a graphics processing unit (GPU), a tensor processing unit (TPU),or an artificial intelligence accelerator microprocessor. Workers canexecute concurrently on a hardware processing unit. Workers can executein parallel across multiple hardware processing units.

The disclosed techniques may encompass performance of a composite modelsearch algorithm. The search algorithm can create a composite model byselecting optimal sub-models using an adaptive learning process tocreate the composite model. The search algorithm can add structurallydiverse sub-models of different depths, widths, and types including, butnot limited to, fully connected neural networks, convolutional neuralnetworks, residual blocks, recurrent neural networks, and user-designedstructures, and at the same time balance the performance of thecomposite model against structural complexity of the composite model.With the disclosed techniques, learning the composite model may be assimple, in terms of hyperparameters, from an end-user's perspective astraining a linear machine learning model.

The search algorithm may operate by iteratively learning multiple,lightweight sub-models that are synchronized to create a compositemodel. However, the search algorithm can confront performance challengeswhen executed on a cluster of multiple workers. In particular, theperformance of the search algorithm on a cluster may be affected by astraggler effect. The straggler effect may result from the learning timeof different sub-models being different with some sub-models takinglonger to learn than others. In addition, the overhead of networkcommunications between workers in the cluster when synchronizing thecomposite model can affect the performance of the search algorithm.

The issues associated with straggler effects and network communicationoverhead during synchronization when executing the search algorithm in adistributed learning computing system may be reduced or mitigated byemploying a network-level asynchronous distributed learning strategythat may scale better with larger clusters in terms of total compositemodel learning time when compared to other distributed learningstrategies. With the network-level asynchronous distributed learningstrategy, sub-models may be learned separately with different shares ofcluster resources according to the complexity of their respectivesub-model architectures. By doing so, the number of workers learning asingle sub-model may be reduced, thereby reducing network communicationsin the cluster. Further, workers training one sub-model need not idlywait for other workers in the cluster to finish learning othersub-models before the workers are scheduled to learn a new sub-model,thereby reducing or mitigation straggler effects.

The network-level asynchronous distributed learning strategy can provideimprovements to a distributed learning computing system including, butnot limited to, the ability to more efficiently explore for an optimalcomposite model structure on large learning datasets and the ability tobetter scale composite model architecture search and hyperparametertuning on a cluster of hardware processors.

Parameter Server Framework

According to some disclosed embodiments, the network-level asynchronousdistributed learning strategy is employed in a parameter serverframework. Learning a composite model can require a large learningdataset on the order, for example, of gigabytes, petabytes, or terabytesin size. Such a learned composite model may encompass parameters (e.g.,model weights and model bias) that, during learning, are optimized forerror during inference. The number of parameters might be on the orderof thousands, millions, billions to even trillions. It may not bepractical or even possible to learn such a large composite model using asingle computing device. Accordingly, a distributed learning computingsystem composed of multiple computing nodes may be needed.

As used herein, the term “computing node” encompasses a physicalcomputing device and may correspond to an operating system instance oran operating system container instance executing on the physicalcomputing device. Multiple operating system container instances canexecute on the physical computing device. Multiple operating systeminstances can execute on the physical computing device with the aid of aType-1 or Type-2 hypervisor. Thus, multiple different computing nodesmay encompass the same physical computing device. However, a one-to-onecorrespondence is also possible.

In a distributed learning computing system, parameters may need to beshared among multiple computing nodes where the parameters are updatedduring execution of the composite model search algorithm on thedistributed learning computing system. The communication over a datacommunications network (e.g., an Internet Protocol (IP)-based datacommunications network) of the large number of parameters among multiplecomputing nodes can be a bottleneck for the performance of the searchalgorithm because of the network bandwidth required to share theparameters and because of the synchronization of parameters betweencomputing nodes that may be needed. In addition, if the computing nodesare implemented using commodity computing devices, then failure ofcomputing nodes should be expected. The parameter server frameworkaddresses these and other issues. The network-level asynchronousdistributed learning strategy disclosed herein that is employed in theparameter server framework further addresses these and other issuesespecially with respect to large-scale learning datasets gigabytes,terabytes, or petabytes in size.

According to some disclosed embodiments, the parameter server frameworkencompasses an asynchronous task model and application programminginterface for reducing overall network bandwidth consumption forlearning a composite model. The framework may reduce the cost ofsynchronization by allowing relaxed consistency. The framework may allowsoftware developers or other technical personnel to choose betweenalgorithm convergence and learning performance. The framework may allowfor adding more horizontal computing capacity without restarting modellearning. The framework may allow for quick (e.g., within seconds)recovery of computing tasks on a computing node that fails. Theframework application programming interface (API) may be structured tosupport machine learning constructs such as sparse vectors, metrices,and tensors.

For example, a supervised learning problem for learning a compositemodel may encompass optimizing a cost function given a learning dataset.Model parameters may be adjusted over learning examples to reduce orminimize the error of inference. Adjustment of model parameters mayencompass computing partial derivatives or gradients. The gradients“move” the model parameters in the right “direction” to minimize thecost function error.

FIG. 4 illustrates example distributed learning computing system 400according to the parameter server framework, according to some disclosedembodiments. System 400 has M number of worker computing nodes 402 (alsosometimes referred to herein as “workers 402”) and parameter servercomputing node 410 (also sometimes referred to herein as “parameterserver 410”). Each worker 402 loads a subset of learning dataset 416with different workers 402 loading different subsets of learning dataset416. For example, worker 402-1 loads learning data subset 408-1 andworker 402-M loads learning data subset 408-M. Although only oneparameter server is depicted in system 400, there may be multipleparameter servers that are each assigned to a partition of a parameterkeyspace that the parameter server is responsible for.

Each worker computes partial gradients on its local learning data subsetfor cost function optimization based on its partial model parameters.For example, worker 402-1 computes partial gradients 404-1 on learningdata subset 408-1 based on partial model parameters 406-1. Worker 402-Mcomputes partial gradients 404-M on learning data subset 408-M based onpartial model parameters 406-M.

Each worker then sends the computed partial gradients to a server. Forexample, worker 402-1 sends computed partial gradients 404-1 toparameter server 410 and worker 402-M pushes computed partial gradients404-M to parameter server 410. Parameter server 410 then aggregates thecomputed partial gradients 404 received from workers 402 to produceaggregated gradients 412 at parameter server 410 and updates modelparameters 414 at parameter server 410 based on aggregated gradients412.

Once parameter server 410 computes aggregated gradients 412 and updatesmodel parameters 414 based thereon, workers 402 can pull updated partialmodel parameters 406 of updated model parameters 414 from server 410 andcompute new partial gradients 404 based on their respective updatedpartial model parameters 406. For example, worker 402-1 can pull updatedpartial model parameters 406-1 of updated model parameters 414 fromserver 410 and worker 402-M can pull updated partial model parameters406-M of updated model parameters 414 from parameter server 410. Worker402-1 can then compute new partial gradients 404-1 on subset 408-1 basedon updated partial model parameters 406-1. Likewise, worker 402-1 canthen compute new partial gradients 404-M on learning data subset 408-Mbased on updated partial model parameters 406-M. This push and pullcycle can repeat for a number of iterations. The number of iterationscan be predefined (e.g., user-specified) or based on a convergencefactor (e.g., amount of error according to model cost function).

Significant computation may be performed at workers 402 computingpartial gradients 404. Because each worker (e.g., 402-1) computespartial gradients (e.g., 404-1) on only a subset (e.g., 408-1) oflearning dataset 416, each worker needs only a subset of all modelparameters 414, which may number into the thousands, millions, billions,or trillions. In particular, each worker (e.g., 402-1) needs only thepartial parameters (e.g., 406-1) pertaining to the learning data subset(e.g., 408-1) on which it computes its partial gradients (e.g., 404-1).In this way, system 400 can scale to learn a composite model based on alarge learning dataset. Further scalability can be achieved by employingthe network-level asynchronous distributed learning strategy describedin greater detail elsewhere in this disclosure.

FIG. 5 is flowchart 500 of a process performed by a worker in adistributed learning system according to the parameter server framework,according to some disclosed embodiments. The worker process may beperformed by each worker in the distributed learning system. There maybe multiple workers in the distributed learning system. Each worker mayperform the worker process iteratively for a number of iterations. Atblock 510, a worker computes partial gradients based on a local learningdata subset for a current iteration. At block 520, the worker pushes thepartial gradients computed to a parameter server for the currentiteration. At block 530, the worker pulls the updated partial modelparameters from the server before the next iteration.

FIG. 6 is flowchart 600 of a process performed by a parameter sever in adistributed learning system according to the parameter server framework,according to some disclosed embodiments. The parameter server processmay be performed by each parameter server in the distributed learningsystem. There may be multiple parameter servers in the distributedlearning system. However, typically there are fewer parameter serversthan there are workers as the workers are used to parallelize theintensive computation of gradients across multiple hardware processors.

Each parameter server may perform the parameter server processiteratively for a number of iterations. At block 610, a serveraggregates the partial gradients from multiple workers for a currentiteration. At block 620, the server computes new model parameters basedon the aggregated partial gradients. For example, computing new modelparameters at block 620 may be based on the current model parameters, alearning rate, the aggregated gradients, and a regularization parameter.

FIG. 7 illustrates the high-level architecture of distributed learningsystem 700, according to some disclosed embodiments. System 700 includesparameter server group 710 and worker groups 720. Server group 710 hasmultiple parameter server computing nodes 410. Each worker group 720 hasmultiple worker computing nodes 402. Each parameter server 410 ofparameter server group 710 is assigned a portion of a parameterkeyspace. Parameter servers 410 may communicate over a datacommunications network for migrating or replicating data for scalabilityand availability. Parameter server manager 712 may maintain a consistentview of parameter server group 710 by performing liveness checks ofparameter servers 410 and assigning partitions of the parameter keyspaceto servers 410.

Multiple workers 402 make up multiple worker groups 720. Workers 402communicate over a data communications network with server group 710 forpulling updated model parameters and pushing computed partial gradientsas described above. According to some disclosed embodiments, workergroups 720 do not communicate with each other. For example, differentworker groups 720 may be assigned to different learning applications.

Each worker group (e.g., 720-2) has a task scheduler (e.g., 722-2). Thetask scheduler assigns learning tasks to workers (e.g., 402-2) in theworker group (e.g. 720-2). A learning task at a worker may includecomputing partial gradients from a local learning data subset, executingkernel computation, and aggregating features within a local learningdata subset. According to some disclosed embodiments, the same workercan use data stored locally at the worker by iteratively processing thesame learning data subset. According to some disclosed embodiments,parameter namespaces can be used for parallelizing learning tasks amongmultiple worker groups 720. According to some disclosed embodiments, aparameter namespace can be shared among multiple worker groups 720. Forexample, one worker group (e.g., 720-1) can support real-time inferencewhile another worker group (e.g., 720-2) can support model learning andupdating of shared model parameters.

More information on the parameter server framework is described in thepaper by Mu Li, David G. Andersen, Jun Woo Park, Alexander J. Smola, AmrAhmed, Vanja Josifovski, James Long, Eugene J. Shekita, Bor-Yiing Su,Scaling Distributed Machine Learning with the Parameter Server,Proceedings of the 2014 International Conference on Big Data Science andComputing, Aug. 4-7, 2014, Beijing China, the entire contents of whichis hereby incorporated by reference.

Composite Neural Network Search Algorithm

According to some disclosed embodiments, a composite neural network iscreated by selecting sub-neural networks and using an adaptive compositeneural network search algorithm to attain the composite neural network.Some theory that underpins the composite neural network search algorithmis described first, followed by a practical workflow clarification.

Theory

The discussion of the theory supporting the composite neural networkmodel search algorithm encompasses the hidden layer family, the neuralnetwork family, and the objective function.

Hidden Layer Family

Let l represent the number of intermediate layers in a network and n_(k)the maximum number of units in layer k. The network can be a compositeneural network or a sub-neural network. Each unit j in layer krepresents a function denoted by h_(k,j). Let x denote the input, andψ(x) denote corresponding feature vector. Then, the family of functionsdefined by the first layer functions h_(1,j) may be represented by thefollowing:H ₁ ={x

u·ψ(x)}.

The family of functions h_(k,j), in a higher layer k may then berepresented as follows:H _(k) ={x

Σ _(s=1) u _(s)·(ψ_(s) ∘h _(s))(x)},

Here, each unit function h_(k,s), u_(s) represents the vector of weightsfor connections from that unit to a lower layer s. And ψ_(s)∘h_(s)represents a coordinate-wise composition:ψ_(s) ∘h _(s)=(ψ_(s) ∘h _(s,1)ψ_(s) ∘h _(s,2), . . . ,ψ_(s) ∘h _(s,ns)),

The ψ_(s) represents a 1-Lipschitz activation function like theRectified Linear Unit function (ReLu function) or the sigmoid function.

Neural Network Family

The output unit can be connected to all intermediate units, whichtherefore defines a function ƒ, which is the so-called neural networksthat are considered as follows:ƒ=Σ_(k=1)Σ_(j=1) w _(k,j) h _(k,j)=Σ_(k=1) w _(k) ·h _(k),

Here, h_(k)=[h_(k,1), h_(k,2), . . . , h_(k,n) _(k) ] and w_(k)represents the vector of connection weights to units of layer k.

Then, F represents the family of functions defined to be the neuralnetworks:F={Σ _(k=1) W _(k) ·h _(k)}.

Objective Function

Let {h₁, h₂, . . . , h_(N)} be a subset of H. The composite neuralnetwork search algorithm seeks to find a function ƒ=Σ_(j=1)w_(j)h_(j), aneural network, that directly minimizes the following objectivefunction:F(w)=λΣ_(i=1)Φ(1−y _(i)Σ_(j=1) w _(j) h _(j))+Σ_(j=1) β|w _(j)|,

Here, Φ represents a loss function such as, for example, the exponentialfunction or softmax function. One of the major advantages to define sucha family of neural networks is that the objective function is a convexfunction of w, which is the sum of a convex surrogate of the empiricalerror and a regularization term to trade off performance and structurecomplexity.

According to some disclosed embodiments, the composite neural networksearch algorithm proceeds in T iterations. At an iteration t, there maybe several sub-neural networks in a sub-neural network candidates poolready to be augmented, and the search algorithm may select one of thefollowing three types of augmentation options:

Augmentation Option 1: Augmenting the current composite neural networkwith a sub-neural network with the same depth as that of the sub-neuralnetworks of the current candidates pool. Each unit in layer k of thissub-neural network may have connections to the existing units in layerk−1 of the current neural network in addition to units in layer k−1 ofthe sub-neural network.

Augmentation Option 2: Augmenting the current neural network with aone-layer-deeper sub-neural network compared to that of the sub-neuralnetworks of the current candidates pool. The set of allowed connectionsis defined the same way as for the first option.

Augmentation Option 3: Augmenting the current neural network with asub-neural network with more units in one layer compared to that of thesub-neural networks of current candidates pool. The set of allowedconnections is defined the same way as for the first option.

The augmentation option that is selected may be the option resulting ina greatest reduction of a current value of a user-designed metricfunction, which could be the loss objective, accuracy, or area under thecurve.

The composite neural network structure after t−1 rounds may berepresented by ƒ_(t-1). And the current sub-neural networks in thecandidates pool is denoted by:{h _(t-1,1) ,h _(t-1,2) , . . . h _(t-1,m)},

In the above and the following, the variable m represents the number ofsub-neural networks in the candidates pool. And newly generatedsub-neural networks in new candidates pool for iteration t isrepresented by:{h _(t-1,1) ,h _(t-1,1) ′,h _(t-1,2) ,h _(t-1,2) ′ . . . ,h _(t-1,m) h_(t-1,m)′}.

Therefore, it is equivalent to minimize the following objective functionat iteration tF(w,u)=λΣ_(i=1)Φ(1−y _(i)ƒ_(t-1)(x _(i))−y _(i) w·u(x _(i)))+β|w|.

FIG. 8 is flowchart 800 of the composite neural network searchalgorithm, according to some disclosed embodiments. At block 810, blocks811, 812, 813, and 814 represent operations performed for each iterationt of a total T number of iterations (e.g., for t: 1→T do . . . ). In thefollowing, S represents the learning dataset exclusive of the testdataset and the user-designed metric function is represented as M.

At block 811, each candidate sub-neural network at the current iterationt is trained separately as in the following pseudo-code:

1: For h in {h_(t,1), h_(t,2), ... , h_(t,m) _(,t+1) }: 2:  h =WeakLearner(S, ƒ_(t−1)) 3:  w = Minimize(F_(t)(w, h))

At block 812, the current neural network at the current iteration t isaugmented and a different composite neural network is tried as in thefollowing pseudo-code:

1: For i, h_(i) in {h_(t,1)*, h_(t,2)*, ... , h_(t,m) _(t+1) * }: 2: ƒ_(t) = ƒ_(t−1) + w_(i) · h_(i) 3:  w_(i) = Minimize(F_(t)(w_(i),h_(i)))

At block 813, a select operation is performed at the current iteration tas in the following pseudo-code:

01: F_(t), h*, w* = Minimize(M, {h_(t,1)*, h_(t,2)*, ... , h_(t,m)_(t+1) *})

At block 814, the set of candidate subnetworks is changed for the nextiteration t+1 as in the following pseudo-code:

01: {h_(t+1,1), h_(t+1,2), ..., h_(t+1,m) _(t+1) } =SelectCandidates({h_(t,1)*, h_(t,2)*, ... , h_(t,m) _(t+1) *})

After all iterations 810 are complete, then the algorithm returns 820 acomposite neural network model ƒ_(T).

One example of a composite model learning algorithm that is used in somedisclosed embodiments it the AdaNet algorithm described in the paper byCorinna Cortes, Xavier Gonzalvo, Vitaly Kuznetsov, Mehryar Mohri, ScottYang, Proceedings of the 34th International Conference on MachineLearning, PMLR 70:874-883, 2017, Sydney, Australia, the entire contentsof which is hereby incorporated by reference.

Learning Workflow

In this section, a more detailed step-by-step description of a possiblelearning workflow is presented, according to some disclosed embodiments.Suppose after t−1 iterations of the composite neural network searchalgorithm, a composite neural network model has been learned and thecandidate pool in iteration t has been filled with small dynamicsub-neural networks.

For example, FIG. 9A shows example composite neural network 902A andexample sub-neural network candidate pool 904A after iteration t−1 ofthe composite neural network search algorithm is complete and beforeiteration t commences, according to some disclosed embodiments.According to some disclosed embodiments, the composite model learningalgorithm may perform the following operations at iteration t.

1) Stack more sub-neural networks to the composite neural network 902Aafter iteration t−1.

2) Select sub-neural networks for the next iteration t+1.

FIG. 9B shows example composite neural network 902B where all of thesub-neural networks in example candidate pool 904B are learnedseparately, according to some disclosed embodiments. Learning separatelymay encompass learning each sub-neural network with the same data inputlayer and a different respective output loss layer, as shown in FIG. 9B.

Composite neural networks may be built between learned sub-neuralnetworks and the composite neural network at the current iteration. Allmodel parameters that have been learned in previous iterations will beinherited as the initialization in the current iteration. To connect thesub-neural network with current composite neural network, newconnections are added from layer k of subnetwork to layer k+1 of thecurrent composite neural network, which is represented by the areabounded by lines 906C in FIG. 9C. FIG. 9C shows current examplecomposite neural network 902C and example candidate pool 904C atiteration t of the composite neural network search algorithm, accordingto some disclosed embodiments. FIG. 9C depicts the construction of a newcomposite neural network using a current composite neural network and acandidate sub-neural network. The best composite neural network afterconsidering the candidates is selected as the new composite neuralnetwork at iteration t. In doing so, previously learned parameters ofsub-neural networks are used as initialization. The composite neuralnetwork is co-learned on extra data steps with newly added weights. Itshould be noted that there is no connection added from layer k of thecurrent composite neural network to layer k+1 of the sub-neural network.

At iteration t, all composite neural networks are evaluated, and thebest composite neural network is retained. All sub-neural networks maybe ranked according the evaluation results and the top sub-neuralnetwork may be retained for the next iteration t+1. New candidatesub-neural networks may be generated based on the best-performingsub-neural networks under specified augmentation options describedabove.

A new composite neural network may be created after iteration t based onthe composite neural network created at iteration t−1 and a newly addedsub-neural network selected from the candidate pool. A new candidatepool is created at iteration t+1 according to the updated evaluationresults of iteration t. Both the composite neural network and thecandidate pool are available for the next iteration t+1. FIG. 9Dillustrates how new sub-neural networks are selected and generated inthe next candidate pool from iteration t to iteration t+1, according tosome disclosed embodiments.

Technical Challenges with Composite Model Search Algorithms

A composite model search algorithm involves iteratively learningmultiple lightweight sub-models and creating composite models basedthereon. To create composite models, models trained on different datapartitions of the learned dataset at different workers in a distributedlearning system must be synchronized to obtain an optimal sub-model.Therefore, in a conventional sequential learning strategy, an expensivecluster-level synchronization of model parameters at the end of eachsub-model learning task may be required. This requirement can be asevere bottleneck to making a composite model search algorithm scalableon a large-scale cluster due to straggler effects and heavy networkcommunication latency during synchronization.

On a cluster with multiple workers in a distributed learning system, astraggler worker may still be working on its share of the parallelizedcomputation when most or all of the other workers have completed theirshares. This uneven worker performance can be termed the stragglereffect, which dramatically slows down the distributed learning process,especially when the capacity of the distributed learning system isrelatively large. The capacity of the distributed learning system can beaffected by a variety of factors including the number of workercomputing nodes, the size of the learning dataset in terms of number ofbytes, and the depth and width of the sub-models (e.g., depth and widthof sub-neural networks). Apart from straggler effect, some otherunpleasant phenomena are observed to cause latencies during distributedcomposite model learning. For example, synchronization time among allworkers can be multiple times more than the computation time.

Ideal Distributed Learning Parallelization in a Distributed LearningSystem

FIG. 10A illustrates ideal distributed composite model learningparallelization in a distributed learning system, according to someembodiments. In this example and other examples provided herein, thereare five worker computing nodes in a worker group of the distributedlearning system. However, in a given implementation there may be more orfewer workers (e.g., twenty workers) in a worker group.

One of the workers (Worker 1) in the worker group is a “chief” workerthat performs model structure adjustment operations of a composite modelsearch algorithm such as, for example, the AdaNet algorithm mentionedabove. Structure adjustment operations may encompass horizontally orvertically stacking sub-models (e.g., sub-neural networks) to form anintermediate or final composite model (e.g., an intermediate or finalcomposite neural network). Another example of a structure adjustmentoperation in the neural network context is generating a new dense, fullyconnected layer to connect multiple sub-neural networks.

Another of the workers (Worker 5) in the worker group is an “evaluation”worker that performs model evaluation operations of the composite modelsearch algorithm. Model evaluation operations may encompass computingrecall, precision, accuracy, F1 score, and/or perplexity scores such as,for example, for a natural language processing task. The modelevaluation operations may be user defined or user specified according tothe requirements of the particular implementation at hand including thetype of machine learning task at hand. Model evaluation operations mayalso encompass measuring the stopwatch time per iteration of thecomposite model search algorithm to monitor computing efficiency of thealgorithm.

Ideally, during a first period of time T1, Workers 1-4 learn a firstsub-model in parallel according to the composite model search algorithm.All Workers 1-4 complete their respective learning tasks at the sametime such that none of the Workers 1-4 must wait for another of theWorkers 1-4 to complete their respective learning task before thesynchronization process can begin at time T3 after time T1.

The synchronization process may involve parameter communication over adata communications network (e.g., an IP-based network) between workernodes in a worker node group. In particular, a worker in the workergroup may communicate its partial model parameters to each of the otherworkers in the worker group that computed partial model parameters. Forexample, at time T3, Worker 1 may communicate its partial modelparameters to each of Workers 2, 3, and 4. Likewise, at time T3, Worker2 may communicate its partial model parameters to each of Workers 1, 3,and 4, Worker 3 may communicate its partial model parameters to each ofWorkers 1, 2, and 4, and Worker 4 may communicate its partial modelparameters to each of Workers 1, 2, and 3. Thus, each of Workers 1-4involved in learning the first sub-model received may each other'spartial model parameters during the synchronization process at time T3.

In addition to, or as an alternative to, exchanging partial modelparameters, the synchronization process may involve exchanging partialgradients and/or other computation results such as, for example,intermediate values. At the start of the synchronization process, eachworker may setup a network communications channel (e.g., a transmissioncontrol protocol (TCP) connection) with each of the other workers. Overthese established communications channels, each worker can receivepartial model parameters, partial gradients, and/or other computationresults from other workers in the worker group. A worker may use theinformation received from other workers during the synchronizationprocess to perform further computation such as, for example, neuralnetwork computation and/or back propagation of gradients.

Once the synchronization process at time T3 is complete, all Workers 1-4learn a second sub-model in parallel according to the composite modelsearch algorithm. During time period T5 after T3, all Workers 1-4complete their respective learning tasks for the second sub-model at thesame time such that none of the Workers 1-4 must wait for another of theWorkers 1-4 to complete their respective learning task for the secondsub-model before the synchronization process can begin at time T7 aftertime T5.

During time period T9 after T7, all Workers 1-4 learn a first compositemodel composed of the first sub-model and the second sub-model inparallel according to the composite model search algorithm. All Workers1-4 complete their respective tasks at the same time such that none ofthe Workers 1-4 must wait for another of the Workers 1-4 to completetheir respective learning task before the synchronization process canbegin at time T11 after time T9. The evaluation Worker 5 is idle untiltime period T9 when the evaluation Worker 5 performs evaluationoperations. The chief Worker 1 performs model structure adjustmentoperations during time T13 while Workers 2-5 are idle.

In the ideal situation, a worker performing a learning task on asub-model need not wait for (be idle while) another worker is stillperforming a learning task on the sub-model. In other words, ideallythere are no stragglers. Also, the network communication overhead duringsynchronization is ideally kept to a minimum. In other words, ideallythe synchronization time is minimized.

Practical Distributed Learning Parallelization in a Distributed LearningSystem

In practice, the learning tasks for a sub-model may take longer for someworkers than other workers. In addition, the synchronization process ofparameters among workers takes time because of the networkcommunications involved.

Following the example of FIG. 10A, FIG. 10B illustrates a practicaldistributed composite model learning parallelization in a distributedlearning system, according to some embodiments. As can be seen, Workers1-3 must wait for Worker 4 to complete its sub-model learning taskbefore the synchronization process at time T3 can begin. Similarly, thesynchronization process at time T7 must wait for straggler Worker 4 tocomplete it sub-model learning task before the synchronization processat time T7 can begin. During this time, Workers 1-3 are idle. Likewise,the synchronization process at time T11 must wait for straggler Worker 3to complete its sub-model learning task before the synchronizationprocess at Time T11 can begin. Meanwhile, Workers 1, 2, and 4 are idle.

Network-Level Asynchronous Distributed Learning Strategy

In order to reduce straggler effect and communication latency duringsynchronization, a network-level asynchronous distributed learningstrategy is used, according to some disclosed embodiments. Inasynchronous distributed training strategy of, workers may performfurther learning tasks immediately after completing a previous learningtask. More specifically, in a cluster with data parallelism, sub-modelsare learned separately with different shares of workers. One worker mayimmediately start a learning task for a next sub-model after completinga learning task for a previous sub-model and need not wait for otherworkers to finish their learning tasks for the previous sub-model.

According to some disclosed embodiments, sub-models may be trainedseparately with different shares of workers according to the complexityof their architectures. Compared to traditional distributed trainingstrategy, the network-level asynchronous distributed learning strategyperforms distributed learning in the level of sub-models to reduce thenumber of individual workers involved in the learning of one sub-model.More specifically, in one iteration of a composite model searchalgorithm such as, for example, the AdaNet algorithm discussed above,sub-models are learned separately in parallel with different shares ofworkers. The number of workers that are allocated to a sub-model mayvary based on the sub-model's structural complexity. For example, thenumber of workers allocated to the sub-model may depend on the width anddepth of the sub-model (e.g., a sub-neural network). For example, if thesub-model is a neural network, the number of workers allocated can bedetermined based on the number of hidden units and the number ofconnections of the neural network. For example, consider threesub-neural networks, one of them, network A, is fully connected and has3 layers where each of the layers has 10 units. Thus, neural network Ahas 30 hidden units in total and 10×10+10×10=200 connections. Two othernetworks, network B and C, are each fully connected and have 2 layers,each of which has 5 units. Thus, each of neural networks B and C eachhas 10 units and 25 connections total. The number of workers allocatedto a sub-neural network can be based on the ratio of hidden layerconnections. For example, if there are M number of workers (e.g.,twenty) in the worker group to which to allocate to sub-neural networksA, B, and C above, then the number of workers in the worker groupallocated to sub-neural networks A, B, and C can be computed as follows:

Example Number of Sub-Neural Workers Allocated Network (M = 20) A M*(200/250) = 16 B M*(25/250) = 2 C M*(25/250) = 2

The number of workers allocated to a sub-neural network can be based onthe ratio of hidden layer units. For example, if there are M number ofworkers (e.g., twenty) in the worker group to which to allocate tosub-neural networks A, B, and C above, then the number of workers in theworker group allocated to sub-neural networks A, B, and C can becomputed as follows:

Example Number of Sub-Neural Workers Allocated Network (M = 20) A M*(30/50) = 12 B M*(10/50) = 4 C M*(10/50) = 5

In comparison, with a conventional distributed learning strategy,learning of sub-models is sequential using all available workers in aworker group, except for possibly an evaluation worker. Therefore,worker group-level synchronization involving all available workers inthe worker group occurs more frequently compared to the network-levelasynchronous distributed learning strategy. In contrast, with thenetwork-level asynchronous strategy, different subsets of all availableworkers in the worker group are used to learn different sub-models,thereby reducing the number of workers involved in a synchronization fora sub-model. By reducing the number of workers involved in asynchronization, the associated network communication overhead in termsof network bandwidth consumed by the synchronization is reduced.

FIG. 11A depicts the conventional distributed learning strategy,according to some embodiments. Learning a first sub-model occupiesWorkers 1-4 for time period T1 from time to to t₁. Learning a secondsub-model occupies Workers 1-4 for time period T5 after time period T1from time t₂ to time t₃. Note that the synchronization process duringtime period T3 and time period T7 occupies all four Workers 1-4.

In contrast, FIG. 11B depicts the network-level asynchronous distributedlearning strategy, according to some embodiments. Learning the secondsub-model occupies only Workers 1, 2 during time period T1, which isless than the four Workers 1-4 available. Learning the first sub-modeloccupies only Workers 3, 4 during time period T1. Because learning thefirst sub-model occupies only two Workers 3, 4 (instead of four Workersas in FIG. 11A), the first synchronization at time t₁′ in FIG. 11B forthe first sub-model has less network communication overhead in terms ofnetwork bandwidth consumed than the synchronization for the firstsub-model at time T3 in FIG. 11A. Also, while the first sub-model islearned by Workers 3, 4, the second sub-model is learned by Workers 1,2. In particular, unlike a conventional distributed learning strategy,sub-models are learned in parallel on different workers.

With a conventional distributed learning strategy, once a sub-modellearning task is completed by a worker, and before the worker groupbegins to build composite models, the worker may be idle while otherworkers (stragglers) in the worker group finish their sub-model learningtasks. This slows the overall execution of the composite model searchalgorithm on the worker group.

FIG. 12 illustrates the straggler effect in a worker group of adistributed learning system where the network-level asynchronousdistributed learning strategy is employed, according to some disclosedembodiments. As shown, Workers 3, 4, each perform a learning task for afirst sub-model during time T1. During time T3 after time T1, asynchronization process for the first sub-model is performed involvingWorkers 3, 4. However, during time T5 after time T3, Workers 3, 4 areidle (e.g., not performing a learning task) while waiting for Workers 1,2 to complete their respective learning tasks for a second sub-model.

According to some disclosed embodiments, to reduce or eliminate thistype of straggler effect, the network-level asynchronous distributedlearning strategy may encompass scheduling a worker in a worker groupthat has completed a learning task for one sub-model to perform alearning task for a new sub-model without waiting for other workers inthe worker group to complete their respective learning tasks. The newsub-model can one for the current iteration of the composite modelsearch algorithm or a predicted candidate sub-model for the nextiteration of the search algorithm. Thus, the network-level asynchronousdistributed learning strategy can facilitate earlier starts of learningcandidate sub-models, compared to a conventional distributed learningapproach.

In the next iteration of the composite model search algorithm, anearly-started sub-model from a prior iteration that is retained in thesub-model candidates pool for the next iteration can be part of acomposite model without requiring further re-learning of theearly-started sub-model at the next iteration. This can significantlyimprove the overall latency of the composite model search algorithm. Anearly-started sub-model from a prior iteration that is not retained inthe sub-model candidates pool for the next iteration can be discarded(abandoned). Consequently, the early-starting of sub-model earning canbe viewed as a trade-off between learning task redundancy and reducingstraggler effects in the gap between the learning of each sub-modelwithin one iteration of the composite model search algorithm.

FIG. 13A depicts a previous iteration of a composite model searchalgorithm according to the network-level asynchronous distributedlearning strategy, according to some embodiments. During time T1,Workers 3, 4 perform respective learning tasks for a first sub-model andWorkers 1, 2 perform respective learning tasks for a second sub-model.After the synchronization process for the first sub-model is complete,Workers 3, 4 are immediately scheduled to perform respective learningtasks for a first early start sub-model during time T3 without waitingfor Workers 1, 2 to complete their respective learning tasks for thesecond sub-model. After the synchronization process for the secondsub-model is complete, Workers 1, 2 are scheduled to perform respectivelearning tasks for a composite sub-model composed of the first sub-modeland the second sub-model. After the synchronization process for thefirst new sub-model is complete after time T3, Workers 3,4 are scheduledto perform respective learning tasks for a second early start sub-modelduring time T5 without waiting for Workers 1, 2, to complete theirrespective learning tasks for the composite sub-model.

FIG. 13B depicts the next iteration of the composite model searchalgorithm after the previous iteration depicted in FIG. 13A, accordingto some disclosed embodiments. In this example, the first early startsub-model was retained in the candidates pool for the next iteration.Because of the early start during the previous iteration, the firstearly start sub-model does not need to be re-learned during the nextiteration. In this example, the second early start sub-model was notretained in the candidates pool for the next iteration, and thus isdiscarded at the next iteration.

Task Scheduler

FIG. 14 illustrates network communications between task scheduler 1402of a worker group in a distributed learning system and worker 1404 inthe worker group implementing the network-level asynchronous distributedlearning strategy, according to some embodiments. For example, in thecontext of distributed learning system 700 of FIG. 7, task scheduler1402 may correspond to task scheduler 722-2 and worker 1404 maycorrespond to a worker in worker group 720-2.

Initially, task scheduler 1402 sets up data communications channel 1410with worker 1404. Task scheduler 1402 may setup similar but separatedata communications channels with other workers in the worker group towhich worker 1404 belongs. Data communications channel 1410 can be atransmission control protocol (TCP) network connection or other type ofbidirectional data communications network connection. Various networkmessages 1411, 1412, 1413, 1414, 1415, and 11416 may be sent betweentask scheduler 1402 and worker 1404 over data communications channel1410 to facilitate the network-level asynchronous distributed learningstrategy. Like messages may be sent between task scheduler 1402 andother words in the worker group over respective data communicationschannels to facilitate the network-level asynchronization distributedlearning strategy.

When worker 1404 is idle or otherwise not performing a machine learningtasks or model synchronization, worker 1404 may ask 1411 task scheduler1402 for work. When task scheduler 1402 is ready to assign a machinelearning task to worker 1404 it may do so via task assignment 1412. Taskassignment 1412 may include an indication of the machine learning taskto be performed (e.g., gradient computation), training hyperparameters(e.g., learning rate, objective function, etc.), and system-levelinformation such as, for example, a kind of distributed storage to use.Worker 1404 may immediately begin performing an assigned machinelearning task upon receiving task assignment 1412 from task scheduler1402. Task assignment 1412 may indicate or specify a time at whichworker 1404 is to begin performance of the assigned machine learningtask.

Worker 1404 may perform a machine learning task at least partially inparallel with other machine learning tasks performed by other workers inthe worker group as assigned by task scheduler 1402. Here, “at leastpartially in parallel” encompasses two or more workers in a worker groupperforming respective machine learning tasks at the same time where themachine learning tasks performed at least partially in parallel can, butneed not, start and/or end at the same time. In other words, two machinelearning tasks can be said to be performed at least partially inparallel if performance of the two machine learning tasks overlaps intime and the two machine learning tasks start at the same or differenttimes and the two machine learning tasks end at the same or differenttimes.

While worker 1404 is performing an assigned machine learning task, taskscheduler 1402 may periodically ask 1413 worker 1404 if worker 1404 hascompleted the task. For example, task scheduler 1402 may ask 1413 worker1404 every few seconds. Worker 1404 may reply with heartbeat 1416 thatindicates to task scheduler 1402 that worker 1404 is still performingthe assigned machine learning task. Heartbeat 1416 may also provideprogress information such as how much (e.g., a percentage or an amount)of the assigned task has been completed or remains to be completed. Onceworker 1404 completes the assigned machine learning task, it may informtask scheduler 1402 that it has finished 1414 the assigned task.

Once task scheduler 1402 has detected that all workers assigned amachine learning task for learning a sub-model have finished (e.g.,1414) their respective tasks, task scheduler 1402 may instruct worker1404 to synchronize 1415 their respective learned portions of thesub-model with the other workers assigned a machine learning task forlearning the sub-model. Once worker 1404 has completed its portion ofthe synchronization with the other workers, it may again ask 1411 for anext machine learning task.

Computing System Implementation

Some disclosed embodiments may encompass performance of a method by acomputing system having one or more processors and storage media. Theone or more processors and the storage media can be provided by one ormore computing devices. The storage media of the computing system canstore one or more computer programs. The one or more programs caninclude instructions configured to perform the method. The instructionsmay be executed by the one or more processors to perform the method.Some disclosed embodiments can encompass one or more non-transitorycomputer-readable media. The one or more non-transitorycomputer-readable media may store the one or more computer programs thatinclude the instructions configured to perform the method. Somedisclosed embodiments can encompass the computing system having the oneor more processors and the storage media storing the one or morecomputer programs that include the instructions configured to performthe method. Some disclosed embodiments can encompass one or more virtualmachines that logically operate on top of one or more computing devicesand emulate hardware. A virtual machine can be a Type-1 or Type-2hypervisor, for example. Operating system virtualization usingcontainers is also possible instead of, or in conjunction with, hardwarevirtualization using hypervisors.

In some disclosed embodiments that encompasses multiple computingdevices, the computing devices may be arranged in a distributed,parallel, clustered or other suitable multi-node computing configurationin which computing devices are continuously, periodically, orintermittently interconnected by one or more data communicationsnetworks (e.g., one or more internet protocol (IP) networks.) Further,it need not be the case that the set of computing devices that executethe instructions be the same set of computing devices that provide thestorage media storing the one or more computer programs, and the setsmay only partially overlap or may be mutually exclusive. For example,one set of computing devices may store the one or more computer programsfrom which another, different set of computing devices downloads the oneor more computer programs and executes the instructions thereof.

Computing Device

FIG. 15 is a block diagram of a computing device 1500 used in somepossible embodiments of the present invention. Computing device 1500includes bus 1502 or other communication mechanism for communicatinginformation, and one or more hardware processors 1504 coupled with bus1502 for processing information.

Hardware processor 1504 may include, for example, one or moregeneral-purpose microprocessors, central processing units (CPUs) orcores thereof, graphics processing units (GPUs), tensor processing units(TPUs), or systems on a chip (SoCs).

Computing device 1500 also includes a main memory 1506, which may beimplemented by one or more volatile memory devices, coupled to bus 1502for storing information and instructions to be executed by processor1504. Main memory 1506 also may be used for storing temporary variablesor other intermediate information during execution of instructions byprocessor 1504.

Computing device 1500 may also include read-only memory (ROM) 1508 orother static storage device coupled to bus 1502 for storing staticinformation and instructions for processor 1504.

A storage system 1510, which may be implemented by one or morenon-volatile memory devices, is provided and coupled to bus 1502 forstoring information and instructions.

Computing device 1500 may be coupled via bus 1502 to display 1512, suchas a liquid crystal display (LCD), a light emitting diode (LED) display,or a cathode ray tube (CRT), for displaying information to a computeruser. Display 1512 may be combined with a touch sensitive surface toform a touch screen display. The touch sensitive surface may be an inputdevice for communicating information including direction information andcommand selections to processor 1504 and for controlling cursor movementon display 1512 via touch input directed to the touch sensitive surfacesuch by tactile or haptic contact with the touch sensitive surface by auser's finger, fingers, or hand or by a hand-held stylus or pen. Thetouch sensitive surface may be implemented using a variety of differenttouch detection and location technologies including, for example,resistive, capacitive, surface acoustical wave (SAW) or infraredtechnology.

Input device 1514, including alphanumeric and other keys, may be coupledto bus 1502 for communicating information and command selections toprocessor 1504.

Another type of user input device may be cursor control 1516, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 1504 and for controllingcursor movement on display 1512. This input device typically has twodegrees of freedom in two axes, a first axis (e.g., x) and a second axis(e.g., y), that allows the device to specify positions in a plane.

Instructions, when stored in non-transitory storage media accessible toprocessor 1504, such as, for example, main memory 1506 or storage system1510, render computing device 1500 into a special-purpose machine thatis customized to perform the operations specified in the instructions.Alternatively, customized hard-wired logic, one or more ASICs or FPGAs,firmware and/or hardware logic which in combination with the computingdevice causes or programs computing device 1500 to be a special-purposemachine.

A computer-implemented process may be performed by computing device 1500in response to processor 1504 executing one or more sequences of one ormore instructions contained in main memory 1506. Such instructions maybe read into main memory 1506 from another storage medium, such asstorage system 1510. Execution of the sequences of instructionscontained in main memory 1506 causes processor 1504 to perform theprocess. Alternatively, hard-wired circuitry may be used in place of orin combination with software instructions to perform the process.

The term “storage media” as used herein refers to any non-transitorymedia that store data and/or instructions that cause a machine tooperate in a specific fashion. Such storage media may comprisenon-volatile media (e.g., storage system 1510) and/or volatile media(e.g., main memory 1506). Non-volatile media includes, for example,read-only memory (e.g., EEPROM), flash memory (e.g., solid-statedrives), magnetic storage devices (e.g., hard disk drives), and opticaldiscs (e.g., CD-ROM). Volatile media includes, for example,random-access memory devices, dynamic random-access memory devices(e.g., DRAM) and static random-access memory devices (e.g., SRAM).

Storage media is distinct from but may be used in conjunction withtransmission media. Transmission media participates in transferringinformation between storage media. For example, transmission mediaincludes coaxial cables, copper wire and fiber optics, including thecircuitry that comprise bus 1502. Transmission media can also take theform of acoustic or light waves, such as those generated duringradio-wave and infra-red data communications.

Computing device 1500 also includes a network interface 1518 coupled tobus 1502. Network interface 1518 provides a two-way data communicationcoupling to a wired or wireless network link 1520 that is connected to alocal, cellular or mobile network 1522. For example, communicationinterface 1518 may be IEEE 802.3 wired “ethernet” card, an IEEE 802.11wireless local area network (WLAN) card, an IEEE 1502.15 wirelesspersonal area network (e.g., Bluetooth) card or a cellular network(e.g., GSM, LTE, etc.) card to provide a data communication connectionto a compatible wired or wireless network. Communication interface 1518may send and receive electrical, electromagnetic or optical signals thatcarry digital data streams representing various types of information.

Network link 1520 typically provides data communication through one ormore networks to other data devices. For example, network link 1520 mayprovide a connection through network 1522 to local computing device 1524that is also connected to network 1522 or to data communicationequipment operated by a network access provider 1526 such as, forexample, an internet service provider or a cellular network provider.Network access provider 1526 in turn provides data communicationconnectivity to another data communications network 1528 (e.g., theinternet). Networks 1522 and 1528 both use electrical, electromagneticor optical signals that carry digital data streams. The signals throughthe various networks and the signals on network link 1520 and throughcommunication interface 1518, which carry the digital data to and fromcomputing device 1500, are example forms of transmission media.

Computing device 1500 can send messages and receive data, includingprogram code, through the networks 1522 and 1528, network link 1520 andcommunication interface 1518. In the internet example, a remotecomputing device 1530 might transmit a requested code for an applicationprogram through network 1528, network 1522 and communication interface1518. The received code may be executed by processor 1504 as it isreceived, and/or stored in storage device 1510, or other non-volatilestorage for later execution.

CONCLUSION

In the foregoing detailed description, some disclosed embodiments havebeen described with reference to numerous specific details that may varyfrom implementation to implementation. The detailed description and thefigures are, accordingly, to be regarded in an illustrative rather thana restrictive sense.

A reference in the detailed description to some disclosed embodiments isnot intended to mean that the embodiment(s) is/are exclusive of otherdisclosed embodiments, unless the context clearly indicates otherwise.Thus, a disclosed embodiment may be combined with one or more otherdisclosed embodiments in a particular combination, unless the contextclearly indicates that the disclosed embodiments are incompatible.

In the foregoing detailed description and in the appended claims,although the terms first, second, etc. are, in some instances, usedherein to describe various elements, these elements should not belimited by these terms. These terms are only used to distinguish oneelement from another. For example, a first user interface could betermed a second user interface, and, similarly, a second user interfacecould be termed a first user interface, without departing from the scopeof the present invention. The first user interface and the second userinterface are both user interfaces, but they are not the same userinterface.

As used in the foregoing detailed description and in the appendedclaims, the singular forms “a,” “an,” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. As used in the foregoing detailed description and in theappended claims, the term “and/or” refers to and encompasses any and allpossible combinations of one or more of the associated listed items.

As used in the foregoing detailed description in the appended claims,the terms “based on,” “according to,” “includes,” “including,”“comprises,” and/or “comprising,” specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof.

The invention claimed is:
 1. A method performed by a computing systemhaving one or more processors, the method comprising: assigning arespective machine learning task for learning a first machine learnedsub-neural network to each worker node in a first plurality of workernodes and assigning a respective machine learning task for learning asecond machine learned sub-neural network to each worker node in asecond plurality of worker nodes such that each worker node in the firstplurality of worker nodes and in the second plurality of worker nodesperforms the respective machine learning task at least partially inparallel with at least one other of the respective machine learningtasks assigned to first plurality and second plurality of worker nodes;based on detecting that the first plurality of worker nodes hascompleted the respective machine learning tasks assigned to the firstplurality of worker nodes, commanding the first plurality of workernodes to perform a synchronization process for the first machine learnedsub-neural network; and based on detecting that the second plurality ofworker nodes has completed the respective machine learning tasksassigned to the second plurality of worker nodes, commanding the secondplurality of worker nodes to perform a synchronization process for thesecond machine learned sub-neural network.
 2. The method of claim 1,further comprising: based on the detecting that the first plurality ofworker nodes have completed the synchronization process for the firstmachine learned sub-neural network, assigning a respective machinelearning task for learning a third machine learned sub-neural network toeach worker node in the first plurality of worker nodes such that eachworker node in the first plurality of worker nodes performs therespective machine learning task for the third machine learnedsub-neural network at least partially in parallel with at least one ofthe respective machine learning tasks for the second machine learnedsub-neural network assigned to the second plurality of worker nodes. 3.The method of claim 2, further comprising: discarding the third machinelearned sub-neural network at an iteration of a composite neural networksearch algorithm.
 4. The method of claim 1, further comprising:selecting a number of worker nodes to perform respective machinelearning tasks for the first machine learned sub-neural network based ona number of hidden layer units of the first machine learned sub-neuralnetwork; and assigning the respective machine learning task for learningthe first machine learned sub-neural network to each worker node in thefirst plurality of worker nodes based on the selected number of workernodes.
 5. The method of claim 1, further comprising: selecting a numberof worker nodes to perform respective machine learning tasks for thefirst machine learned sub-neural network based on a number of hiddenlayer connections of the first machine learned sub-neural network; andassigning the respective machine learning task for learning the firstmachine learned sub-neural network to each worker node in the firstplurality of worker nodes based on the selected number of worker nodes.6. The method of claim 1, further comprising: causing a composite neuralnetwork to be generated according to a composite neural network searchalgorithm based on the first machine learned sub-neural network and thesecond machine learned sub-neural network.
 7. The method of claim 1,wherein the method is performed by a task scheduler of a worker group ofa distributed learning system according to a parameter server framework,the worker group comprising the first plurality of worker nodes and thesecond plurality of worker nodes.
 8. One or more non-transitorycomputer-readable media storing one or more programs and configured forexecution by a computing system having one or more processors, the oneor more programs comprising instructions which, when executed by the oneor more processors, cause the computing system to perform operationscomprising: assigning a respective machine learning task for learning afirst machine learned sub-model to each worker node in a first pluralityof worker nodes and assigning a respective machine learning task forlearning a second machine learned sub-model to each worker node in asecond plurality of worker nodes such that each worker node in the firstplurality of worker nodes and in the second plurality of worker nodesperforms the respective machine learning task at least partially inparallel with at least one other of the respective machine learningtasks assigned to first plurality and second plurality of worker nodes;based on detecting that the first plurality of worker nodes hascompleted the respective machine learning tasks assigned to the firstplurality of worker nodes, commanding the first plurality of workernodes to perform a synchronization process for the first machine learnedsub-model; and based on detecting that the second plurality of workernodes has completed the respective machine learning tasks assigned tothe second plurality of worker nodes, commanding the second plurality ofworker nodes to perform a synchronization process for the second machinelearned sub-model.
 9. The one or more non-transitory computer-readablemedia of claim 8, wherein the instructions, when executed by the one ormore processors, further cause the computing system to performoperations comprising: based on the detecting that the first pluralityof worker nodes have completed the synchronization process for the firstmachine learned sub-model, assigning a respective machine learning taskfor learning a third machine learned sub-model to each worker node inthe first plurality of worker nodes such that each worker node in thefirst plurality of worker nodes performs the respective machine learningtask for the third machine learned sub-model at least partially inparallel with at least one of the respective machine learning tasks forthe second machine learned sub-model assigned to the second plurality ofworker nodes.
 10. The one or more non-transitory computer-readable mediaof claim 9, wherein the instructions, when executed by the one or moreprocessors, further cause the computing system to perform operationscomprising: discarding the third machine learned sub-model at aniteration of a composite model search algorithm.
 11. The one or morenon-transitory computer-readable media of claim 8, wherein theinstructions, when executed by the one or more processors, further causethe computing system to perform operations comprising: selecting anumber of worker nodes to perform respective machine learning tasks forthe first machine learned sub-model based on a width of the firstmachine learned sub-model; and assigning the respective machine learningtask for learning the first machine learned sub-model to each workernode in the first plurality of worker nodes based on the selected numberof worker nodes.
 12. The one or more non-transitory computer-readablemedia of claim 8, wherein the instructions, when executed by the one ormore processors, further cause the computing system to performoperations comprising: selecting a number of worker nodes to performrespective machine learning tasks for the first machine learnedsub-model based on a depth of the first machine learned sub-model; andassigning the respective machine learning task for learning the firstmachine learned sub-model to each worker node in the first plurality ofworker nodes based on the selected number of worker nodes.
 13. The oneor more non-transitory computer-readable media of claim 8, wherein theinstructions, when executed by the one or more processors, further causethe computing system to perform operations comprising: causing acomposite model to be generated according to a composite model searchalgorithm based on the first machine learned sub-model and the secondmachine learned sub-model.
 14. The one or more non-transitorycomputer-readable media of claim 8, wherein the first machine learnedsub-model is a first machine learned neural network; and wherein thesecond machine learned sub-model is a second machine learned neuralnetwork.
 15. A computing system comprising: storage media; one or moreprocessors; and one or more programs stored in the storage media andconfigured for execution by the one or more processors, the one or moreprograms comprising instructions which, when executed by the one or moreprocessors, cause the computing system to perform operations comprising:assigning a respective machine learning task for learning a firstmachine learned sub-model to each worker node in a first plurality ofworker nodes and assigning a respective machine learning task forlearning a second machine learned sub-model to each worker node in asecond plurality of worker nodes such that each worker node in the firstplurality of worker nodes and in the second plurality of worker nodesperforms the respective machine learning task at least partially inparallel with at least one other of the respective machine learningtasks assigned to first plurality and second plurality of worker nodes;based on detecting that the first plurality of worker nodes hascompleted the respective machine learning tasks assigned to the firstplurality of worker nodes, commanding the first plurality of workernodes to perform a synchronization process for the first machine learnedsub-model; and based on detecting that the second plurality of workernodes has completed the respective machine learning tasks assigned tothe second plurality of worker nodes, commanding the second plurality ofworker nodes to perform a synchronization process for the second machinelearned sub-model.
 16. The computing system of claim 15, wherein theinstructions, when executed by the one or more processors, further causethe computing system to perform operations comprising: based on thedetecting that the first plurality of worker nodes have completed thesynchronization process for the first machine learned sub-model,assigning a respective machine learning task for learning a thirdmachine learned sub-model to each worker node in the first plurality ofworker nodes such that each worker node in the first plurality of workernodes performs the respective machine learning task for the thirdmachine learned sub-model at least partially in parallel with at leastone of the respective machine learning tasks for the second machinelearned sub-model assigned to the second plurality of worker nodes. 17.The computing system of claim 16, wherein the instructions, whenexecuted by the one or more processors, further cause the computingsystem to perform operations comprising: discarding the third machinelearned sub-model at an iteration of a composite model search algorithm.18. The computing system of claim 15, wherein the instructions, whenexecuted by the one or more processors, further cause the computingsystem to perform operations comprising: selecting a number of workernodes to perform respective machine learning tasks for the first machinelearned sub-model based on a width of the first machine learnedsub-model; and assigning the respective machine learning task forlearning the first machine learned sub-model to each worker node in thefirst plurality of worker nodes based on the selected number of workernodes.
 19. The computing system of claim 15, wherein the instructions,when executed by the one or more processors, further cause the computingsystem to perform operations comprising: selecting a number of workernodes to perform respective machine learning tasks for the first machinelearned sub-model based on a depth of the first machine learnedsub-model; and assigning the respective machine learning task forlearning the first machine learned sub-model to each worker node in thefirst plurality of worker nodes based on the selected number of workernodes.
 20. The computing system of claim 15, wherein the instructions,when executed by the one or more processors, further cause the computingsystem to perform operations comprising: causing a composite model to begenerated according to a composite model search algorithm based on thefirst machine learned sub-model and the second machine learnedsub-model.